@article{pope_ellwein_zapata_novak_kelley_olufsen_2009, title={ESTIMATION AND IDENTIFICATION OF PARAMETERS IN A LUMPED CEREBROVASCULAR MODEL}, volume={6}, ISSN={["1551-0018"]}, DOI={10.3934/mbe.2009.6.93}, abstractNote={This study shows how sensitivity analysis and subset selection can be employed in a cardiovascular model to estimate total systemic resistance, cerebrovascular resistance, arterial compliance, and time for peak systolic ventricular pressure for healthy young and elderly subjects. These quantities are parameters in a simple lumped parameter model that predicts pressure and flow in the systemic circulation. The model is combined with experimental measurements of blood flow velocity from the middle cerebral artery and arterial finger blood pressure. To estimate the model parameters we use nonlinear optimization combined with sensitivity analysis and subset selection. Sensitivity analysis allows us to rank model parameters from the most to the least sensitive with respect to the output states (cerebral blood flow velocity and arterial blood pressure). Subset selection allows us to identify a set of independent candidate parameters that can be estimated given limited data. Analyses of output from both methods allow us to identify five independent sensitive parameters that can be estimated given the data. Results show that with the advance of age total systemic and cerebral resistances increase, that time for peak systolic ventricular pressure is increases, and that arterial compliance is reduced. Thus, the method discussed in this study provides a new methodology to extract clinical markers that cannot easily be assessed noninvasively.}, number={1}, journal={MATHEMATICAL BIOSCIENCES AND ENGINEERING}, author={Pope, Scott R. and Ellwein, Laura M. and Zapata, Cheryl L. and Novak, Vera and Kelley, C. T. and Olufsen, Mette S.}, year={2009}, month={Jan}, pages={93–115} }
 @article{ellwein_tran_zapata_novak_olufsen_2008, title={Sensitivity analysis and model assessment: Mathematical models for arterial blood flow and blood pressure}, volume={8}, ISSN={["1573-6806"]}, DOI={10.1007/s10558-007-9047-3}, abstractNote={The complexity of mathematical models describing the cardiovascular system has grown in recent years to more accurately account for physiological dynamics. To aid in model validation and design, classical deterministic sensitivity analysis is performed on the cardiovascular model first presented by Olufsen, Tran, Ottesen, Ellwein, Lipsitz and Novak (J Appl Physiol 99(4):1523-1537, 2005). This model uses 11 differential state equations with 52 parameters to predict arterial blood flow and blood pressure. The relative sensitivity solutions of the model state equations with respect to each of the parameters is calculated and a sensitivity ranking is created for each parameter. Parameters are separated into two groups: sensitive and insensitive parameters. Small changes in sensitive parameters have a large effect on the model solution while changes in insensitive parameters have a negligible effect. This analysis was successfully used to reduce the effective parameter space by more than half and the computation time by two thirds. Additionally, a simpler model was designed that retained the necessary features of the original model but with two-thirds of the state equations and half of the model parameters.}, number={2}, journal={CARDIOVASCULAR ENGINEERING}, author={Ellwein, Laura M. and Tran, Hien T. and Zapata, Cheryl and Novak, Vera and Olufsen, Mette S.}, year={2008}, month={Jun}, pages={94–108} }
 @article{olufsen_ottesen_tran_ellwein_lipsitz_novak_2005, title={Blood pressure and blood flow variation during postural change from sitting to standing: model development and validation}, volume={99}, ISSN={["1522-1601"]}, DOI={10.1152/japplphysiol.00177.2005}, abstractNote={ Short-term cardiovascular responses to postural change from sitting to standing involve complex interactions between the autonomic nervous system, which regulates blood pressure, and cerebral autoregulation, which maintains cerebral perfusion. We present a mathematical model that can predict dynamic changes in beat-to-beat arterial blood pressure and middle cerebral artery blood flow velocity during postural change from sitting to standing. Our cardiovascular model utilizes 11 compartments to describe blood pressure, blood flow, compliance, and resistance in the heart and systemic circulation. To include dynamics due to the pulsatile nature of blood pressure and blood flow, resistances in the large systemic arteries are modeled using nonlinear functions of pressure. A physiologically based submodel is used to describe effects of gravity on venous blood pooling during postural change. Two types of control mechanisms are included: 1) autonomic regulation mediated by sympathetic and parasympathetic responses, which affect heart rate, cardiac contractility, resistance, and compliance, and 2) autoregulation mediated by responses to local changes in myogenic tone, metabolic demand, and CO2 concentration, which affect cerebrovascular resistance. Finally, we formulate an inverse least-squares problem to estimate parameters and demonstrate that our mathematical model is in agreement with physiological data from a young subject during postural change from sitting to standing. }, number={4}, journal={JOURNAL OF APPLIED PHYSIOLOGY}, author={Olufsen, MS and Ottesen, JT and Tran, HT and Ellwein, LM and Lipsitz, LA and Novak, V}, year={2005}, month={Oct}, pages={1523–1537} }